As of the census[9] of 2000, there were 2,240 people, 922 households, and 614 families residing in the county. The population density was 1 people per square mile (0/km²). There were 1,307 housing units at an average density of 1 per square mile (0/km²). The racial makeup of the county was 84.02% White, 0.04% Black or African American, 0.94% Native American, 0.22% Asian, 12.54% from other races, and 2.23% from two or more races. 35.27% of the population were Hispanic or Latino of any race.

There were 922 households out of which 27.20% had children under the age of 18 living with them, 56.60% were married couples living together, 7.30% had a female householder with no husband present, and 33.30% were non-families. 30.80% of all households were made up of individuals and 18.00% had someone living alone who was 65 years of age or older. The average household size was 2.35 and the average family size was 2.96.

In the county the population was spread out with 24.10% under the age of 18, 5.70% from 18 to 24, 21.70% from 25 to 44, 23.20% from 45 to 64, and 25.40% who were 65 years of age or older. The median age was 44 years. For every 100 females there were 96.00 males. For every 100 females age 18 and over, there were 92.10 males.

The median income for a household in the county was $25,441, and the median income for a family was $32,870. Males had a median income of $25,833 versus $18,487 for females. The per capita income for the county was $14,065. 17.70% of the population and 13.60% of families were below the poverty line. Out of the total people living in poverty, 23.30% are under the age of 18 and 15.00% are 65 or older.